Member-only story
Hello, this is Andy. I’m here to tell you about a minor problem in the way the world is. Humor me, your well-adjusted benevolent author, and take a moment to look at the following pictures of shapes.
Aren’t these shapes just the neatest things? They’re so polite, perfectly tiling the imaginary, infinite plane they’re lying on.
Their corner angles piece together so neatly, leaving nothing showing of the mathematical void behind them.
Now, bear with me in considering the shape of the common waffle:
Notice something wrong? Not only are we resorting to putting square indents in a circular object, they don’t even fill the box they’re in properly! Everything about waffles screams “TILE AN INFINITE PLANE WITH ME,” yet Big Breakfast refuses to heed the call of efficient packaging. They’re playing a dangerous game.
In 1611, Johannes Kepler proposed a theoretical maximum density for packing spheres in 3D space. Regardless of how they were arranged in a box, he said, you will never fill more than 74% of your total box volume. His theorem went unproven until 1996, when Thomas Hales made a computer test every…
